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A multi-index model for quantile regression with ordinal data

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  • Hyokyoung Grace Hong
  • Jianhui Zhou

Abstract

In this paper, we propose a quantile approach to the multi-index semiparametric model for an ordinal response variable. Permitting non-parametric transformation of the response, the proposed method achieves a root- n rate of convergence and has attractive robustness properties. Further, the proposed model allows additional indices to model the remaining correlations between covariates and the residuals from the single-index, considerably reducing the error variance and thus leading to more efficient prediction intervals (PIs). The utility of the model is demonstrated by estimating PIs for functional status of the elderly based on data from the second longitudinal study of aging. It is shown that the proposed multi-index model provides significantly narrower PIs than competing models. Our approach can be applied to other areas in which the distribution of future observations must be predicted from ordinal response data.

Suggested Citation

  • Hyokyoung Grace Hong & Jianhui Zhou, 2013. "A multi-index model for quantile regression with ordinal data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(6), pages 1231-1245, June.
    • Handle: RePEc:taf:japsta:v:40:y:2013:i:6:p:1231-1245
    DOI: 10.1080/02664763.2013.785489
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    References listed on IDEAS

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    1. Hong, Hyokyoung Grace & He, Xuming, 2010. "Prediction of Functional Status for the Elderly Based on a New Ordinal Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 930-941.
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